OP - there's no two ways about it. Your child is severely overtired.
No offence intended but I urge you not to take the advice from @PucePanther below because it really isn't necessary. EVERY HUMAN NEEDS SLEEP. Especially babies. I've worked with children for a very very long time and I am yet to meet a single child that doesn't need day sleep at 11 months. Are there children that fight it more than others? Categorically less. But do they all need it regardless? Categorically yes.
I'm not sure if you knew but humans aren't born with the ability to fall asleep themselves. This is something we must all learn, in a similar way that we learn to walk and talk, it's through practice that we learn how to fall asleep and stay asleep by ourselves. A great deal of this depends on our parents and the tools they give us to enable us to learn to fall asleep. Some parents choose to leave this until their children are older and thus understand the concept of "going to sleep". It's not that they just suddenly "got it" when they got older, it's that by the time they learn to fall asleep unaided and stay asleep, they're old enough to understand what that means. They're old enough to understand that it's bedtime. At 11m your child isn't enough enough to understand that concept so it's down to you to encourage them to learn how to sleep, ideally without you.
A HUGE part of this will be a routine because that's the way young children start to understand. Your baby knows that being put in his high chair means it's time to eat, because that's what you've taught him through repetition and routine. Not every parent is a fan of a routine, and that's ok because some parents are happy to let their child do things the way they want to, sleep when they want etc and it works for them and their family. Clearly, this isn't working for you.
At 11m most children have two naps. One longer morning nap, and a top up nap in the afternoon, around 2-3 hours day sleep is needed at that age. As baby gets older they will naturally start fighting the second nap, at which point you can move the morning nap later and later until it's in the middle of the day.
Inevitably there will be a degree of sleep training involved, it's unavoidable. But before the co-sleeping army get in my face, this doesn't need to involve crying. There are some excellent stay and support type methods by sleep experts like Lucy Woolfe that do not involve any crying, but they help your baby learn how to fall asleep and stay asleep.
If there's one thing you take away from this thread, it's that your baby CATEGORICALLY needs day sleep, he just fights it because it's unfamiliar and he's so dog tired by now that it makes it so so much harder to fall asleep. Look into Lucy woolfe but your first step is to definitely fix the day sleep, night sleep will follow once your naps are sorted.
For context, my 19m old son sleeps 7pm-7:30am. He often wakes later but id say that's average. He goes down for a nap at 12:30 and I wake him at 3pm. He was breastfed and slept from 7-7 from 4 months with an 11pm feed until he was 6 months. We have never left him to cry as a form of sleep training.
My sisters have 5 children between them. All of them followed the same routine and have all slept very much the same with varying nap / wakeup times over the years but broadly similar. It annoys me when mothers claim their children "just don't sleep"'when the reality is that they've never allowed them the opportunity to learn.